article published yes Benedikt Groever author Charles Roques-Carmes author e2e68fc9-6505-11ef-a541-eb4e72cc3e82 Steven J. Byrnes author Federico Capasso author Meta-lenses based on flat optics enabled a fundamental shift in lens production—providing an easier manufacturing process with an increase in lens profile precision and a reduction in size and weight. Here we present an analytical approach to correct spherical aberrations caused by light propagation through the substrate by adding a substrate-corrected phase profile, which differs from the original hyperbolic one. A meta-lens encoding the new phase profile would yield diffraction-limited focusing and an increase of up to 0.3 of its numerical aperture without changing the radius or focal length. In tightly focused laser spot applications such as direct laser lithography and laser printing, a substrate-corrected meta-lens can reduce the spatial footprint of the meta-lens. Optica Publishing Group2018 eng 1559-128X 2155-3165 2971432510.1364/ao.57.002973 57122973-2980 yes Groever B, Roques-Carmes C, Byrnes SJ, Capasso F. 2018. Substrate aberration and correction for meta-lens imaging: An analytical approach. Applied Optics. 57(12), 2973–2980. Groever, Benedikt, Charles Roques-Carmes, Steven J. Byrnes, and Federico Capasso. “Substrate Aberration and Correction for Meta-Lens Imaging: An Analytical Approach.” <i>Applied Optics</i>. Optica Publishing Group, 2018. <a href="https://doi.org/10.1364/ao.57.002973">https://doi.org/10.1364/ao.57.002973</a>. B. Groever, C. Roques-Carmes, S.J. Byrnes, F. Capasso, Applied Optics 57 (2018) 2973–2980. Groever B, Roques-Carmes C, Byrnes SJ, Capasso F. Substrate aberration and correction for meta-lens imaging: An analytical approach. <i>Applied Optics</i>. 2018;57(12):2973-2980. doi:<a href="https://doi.org/10.1364/ao.57.002973">10.1364/ao.57.002973</a> B. Groever, C. Roques-Carmes, S. J. Byrnes, and F. Capasso, “Substrate aberration and correction for meta-lens imaging: An analytical approach,” <i>Applied Optics</i>, vol. 57, no. 12. Optica Publishing Group, pp. 2973–2980, 2018. Groever, B., Roques-Carmes, C., Byrnes, S. J., &#38; Capasso, F. (2018). Substrate aberration and correction for meta-lens imaging: An analytical approach. <i>Applied Optics</i>. Optica Publishing Group. <a href="https://doi.org/10.1364/ao.57.002973">https://doi.org/10.1364/ao.57.002973</a> Groever, Benedikt, et al. “Substrate Aberration and Correction for Meta-Lens Imaging: An Analytical Approach.” <i>Applied Optics</i>, vol. 57, no. 12, Optica Publishing Group, 2018, pp. 2973–80, doi:<a href="https://doi.org/10.1364/ao.57.002973">10.1364/ao.57.002973</a>. 215872026-03-30T12:22:48Z2026-04-27T08:41:20Z